Is it permissible to pray in high heels (10-12 cm) to alleviate heel pain, knowing that the heel does not touch the ground, and is it permissible to walk in them on the street while covering them with a garment?

Some scholars disliked wearing high heels because they reveal a woman's charms, cause her health problems, and give the illusion that she is taller than she is. Some have gone further, deeming it disliked (makruh) or forbidden (haram) because it is a form of tabarruj (display of adornment).

As for your situation, if it is medically proven that the pain does not subside except by wearing them, then there is no harm upon you, provided that it does not involve tabarruj or attract the attention of men.

It is permissible to pray in high heels if they are free from impurity.